Problem Euler S Totient Function N Denotes Set Natrual Numbers Prime Number P K N Derive Q37130490

This problem is about Euler’s totient function φ(·). N denotesthe set of natrual numbers. For any prime number p and k ∈ N,derive the expression for φ(p k ).

Related to textbook: Introduction of Modern Cryptography byJonathan Katz

Solution

Follow 1st property if you want to derive .

and 2nd property if you want to derive  .

I have derived both and one generalized derivation for anynumber using both properties.

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